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arXiv · 1902.07925

A structure-preserving Fourier pseudo-spectral linearly implicit scheme for the space-fractional nonlinear Schr\"odinger equation

Yuto Miyatake·Tai Nakagawa·Tomohiro Sogabe·Shao-Liang Zhang
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Abstract

We propose a Fourier pseudo-spectral scheme for the space-fractional nonlinear Schr\"odinger equation. The proposed scheme has the following features: it is linearly implicit, it preserves two invariants of the equation, its unique solvability is guaranteed without any restrictions on space and time step sizes. The scheme requires solving a complex symmetric linear system per time step. To solve the system efficiently, we also present a certain variable transformation and preconditioner.

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Yuto Miyatake, Tai Nakagawa, Tomohiro Sogabe, Shao-Liang Zhang. 2019-02-21. A structure-preserving Fourier pseudo-spectral linearly implicit scheme for the space-fractional nonlinear Schr\"odinger equation. https://arxiv.org/abs/1902.07925

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